Kolmogorov Smirnov Test in Spark (Python) not work

Question

I was doing a normality test in Python spark-ml and saw what I think is an bug.

Here is the setup, i have a data-set that is normalized (range -1, to 1).

When I do a histogram, i can clearly see that the data is NOT normal:

>>> prices_norm.histogram(10)

([-1.0, -0.8, -0.6, -0.4, -0.2, 0.0, 0.2, 0.4, 0.6, 0.8, 1.0],
 [226, 269, 119, 95, 52, 26, 8, 2, 2, 5])

When I run the Kolmgorov-Smirnov test I get the following results:

>>> testResults = Statistics.kolmogorovSmirnovTest(prices_norm, "norm")
>>> print testResults

Kolmogorov-Smirnov test summary:
degrees of freedom = 0 
statistic = 0.46231145770077375 
pValue = 1.742039845709087E-11 
Very strong presumption against null hypothesis: Sample follows theoretical distribution.

The Kolmgorov-Smirnov test defines the null hypothesis (H0) as: the data follows a specified distribution (http://www.itl.nist.gov/div898/handbook/eda/section3/eda35g.htm).

In this case the p-value is very low, so we should reject the null hypothesis. This makes sense, as it is clearly not normal.

So why then, does it say:

Sample follows theoretical distribution

Isn't this wrong? Shouldn't it say that the sample does NOT follow a theoretical distribution? Am I missing something?

Answer 1

This was driving me crazy, so I went to look at the source code directly:

git://git.apache.org/spark.git
spark/mllib/src/main/scala/org/apache/spark/mllib/stat/test/KolmogorovSmirnovTest.scala

The code is correct, the null Hypothesis is set as:

object NullHypothesis extends Enumeration {
  type NullHypothesis = Value
  val OneSampleTwoSided = Value("Sample follows theoretical distribution")
}

The verbiage of the string message is just restating the null hypothesis:

Very strong presumption against null hypothesis: Sample follows theoretical distribution.
                                                 ________________________________________
                                                                    H0

Arguably the verbiage is confusing as it could be interpreted both ways. But it is indeed correct.